Jeff, while I agree with your premise (that a well-design boat from a lucky or talented designer does not have to change balance when heeled) I totally disagree with your ice cream cone analogy.
The analogy should be to a cheese wedge, a slice of cake, or something similar and NOT something with the symmetry of an ice cream cone. The effect of balance and rotation on a symmetrical body like an ice cream cone, will be totally unlike that on a "wedge" like a boat.
And when all else is said and done, a well balanced hull, one that stays in balance in a wide range of conditions including heel, is still as much a gift from the g-ds as it is the work of any designer. Even Bob has said, once upon a time, that he was pleasantly amazed at how well some boats balanced.
I chose to use a cone for my explanation because a cone is very easy to visualize as it rotates and because the reason that a cone remains in trim, i.e. that the buoyancy distribution remains the same, is actually the very same reason that a well modeled beamy boat would remain in trim as it heels.
That said, neither rotating a wedge shaped slab or a cone would behave precisely the same as beamy boat being rotated, but the cone actually behaves closer and uses the same principles. The point that I was trying to make is that by tweaking the rocker, bilge radius, and curvature of the topside in plan and section, a skilled designer can keep the trim essentially the same by keeping the buoyancy the same.
I also respectfully disagree with your comment," a well balanced hull, one that stays in balance in a wide range of conditions including heel, is still as much a gift from the g-ds as it is the work of any designer." I would echo what Bob says above about an experienced designer being able to eyeball and get things close to right the very first time. I am not a professional by a long shot. If there are shortfalls in the drawings within this thread, they come from my limitations as an amateur, operator error, and the limitations of the 2D software that I am drawing with. The fact that they are not a whole lot worse is because Bob is doing his best to keep my out of trouble.
One of the things that I have learned in this process is how quickly Bob can simply look at drawing and spot items that are out of wack even a small amount. When I have calculated some of these items I have been amazed at the precision of his experienced eyeballing.
But back to your comment, the better yacht design houses who are working with these super wide boats, have done enough of these that they too are coming to each design with an eye for what approximately works from the very first draft.
But professional yacht designers also have the benefit of very sophisticated 3D programs which can quickly calculate changes in trim at any heel angle almost on the fly. This allows the designer to tweak the shape of the topsides and bottom to keep the boat in trim as she heels and check their work as they go.
When a designer pushes a design towards the outer limits of conventional design, they become increasingly depended on have great computational tools to check their work rather than relying on luck. But even here, it is the skill of the designer that understands how much of these calculated results really can be relied on.
To me it comes down to my Olin Stephen's quote above about towing tanks, which essentially was that it still requires a skilled designer to design the model that gets towed. For all of the modern tools to validate and take some of the luck out of the equation, the reality is that it still takes a skilled designer with a good eye, to know what to put in the computer.